摘要 : A quantitative version of an inequality obtained in [8, Theorem 2.1] is given. More precisely, for normalized K quasiconformal (q.c.) harmonic mappings of the unit disk onto a Jordan domain Ω ∈ C~(1,μ) (0 < μ ≤ 1), we give an expl... 展开 A quantitative version of an inequality obtained in [8, Theorem 2.1] is given. More precisely, for normalized K quasiconformal (q.c.) harmonic mappings of the unit disk onto a Jordan domain Ω ∈ C~(1,μ) (0 < μ ≤ 1), we give an explicit Lipschitz constant depending on the structure of Ω and on K. In addition, we give a characterization of q.c. harmonic mappings of the unit disk onto an arbitrary Jordan domain with C~(2,α) boundary in terms of the boundary function using the Hilbert transform. Moreover, a sharp explicit quasiconformal constant is given in terms of the boundary function. 收起